Ok, a couple of favorite diner scenes which come to mind:
-Luke and Lorelai prep the diner for a paint job, and Luke talks about his father and shows Lorelai the spot where he took an order ..'Let's not spruce this particular spot'-TDDR
-Rory goes to Luke's in the aftermath of the car accident, and gets there just as he's returning from his fishing trip. He invites her in and they talk about Jess: 'Luke, it wasn't his fault', 'I know it wasn't'-Help Wanted
-Luke hires Lane and she begins to work at the diner: 'When it was slow she cleaned the menus... without being asked', 'I don't even know why she took the job, I totally blew the interview'-The Nanny and The Professor
( I realize there's a good chance this will be voted out immediately since it's from the revival, but I actually really love this scene, so I'm going for it)
-Taylor comes into the diner trying to get Luke to offer a testimonial for his proposed change to a sewer system, Luke refuses, and the typical Luke/Taylor banter ensues. Meanwhile, Luke is purposely giving customers fake WiFi passwords as they keep asking. Suddenly Taylor snaps, goes on a Luke-like rant about WiFi, and leaves. Luke follows him out and tells him he'll help him. Snow starts to fall as they wave goodbye to each other-Winter